Assigning a Molecule with 2D NMR

Introduction

Each 2D experiment answers one kind of question. COSY shows which protons are coupled, HSQC which proton sits on which carbon, HMBC which carbons lie two or three bonds from a proton, and NOESY which protons are close in space. Solving a real structure means combining them in a disciplined order, cross-checking every step and resisting the temptation to fit the data to an expected answer. This page sets out a workflow that chemists use daily and applies it to a small example.

Core explanation

Stage 1: the inventory. Start with the molecular formula, usually from high-resolution mass spectrometry, and calculate the degree of unsaturation. Record the 1D ¹H spectrum with integrals and the ¹³C spectrum. The goal is a complete list of atoms: how many carbons, how many protons on each, and which heteroatoms are present.

Stage 2: attach protons to carbons with HSQC. Every proton is matched with its carbon, and edited HSQC classifies CH, CH₂ and CH₃. Carbons in the ¹³C spectrum with no HSQC partner are quaternary or carbonyl carbons. Any proton with no HSQC peak is attached to a heteroatom (OH, NH). Diastereotopic CH₂ pairs are flagged. At this point the atom list becomes a list of labelled CHₙ units.

Stage 3: build spin systems with COSY (and TOCSY). Starting from resolved signals, walk the coupling networks to connect CHₙ units into chains. Each chain is a fragment. Its ends lie at quaternary carbons, carbonyl groups, heteroatoms or ring junctions. Coupling constants from the 1D spectrum help here: a ³J of about 16 Hz across a C=C indicates E geometry, about 11 Hz Z geometry.

Stage 4: connect fragments with HMBC. Look for protons at the ends of fragments that correlate with carbons outside them, especially quaternary and carbonyl carbons. Methyl singlets are valuable anchors. Where protons from two fragments correlate with the same quaternary carbon, that carbon usually joins them. Characteristic shifts guide placement of heteroatoms: ester carbonyl near 170 ppm, ketone near 205 ppm, carbon bonded to oxygen at 60–80 ppm.

Stage 5: stereochemistry with NOESY or ROESY and J values. Once the connectivity is fixed, spatial contacts establish relative configuration: which substituents share a ring face, whether a double bond is E or Z when J is unavailable, and preferred conformation.

Stage 6: verification. Draw the proposed structure and go back through every correlation. Every HMBC peak should correspond to a two- or three-bond relationship; every strong NOE to a short distance in a reasonable conformer; every shift should be plausible, ideally checked with prediction software or calculation. Then ask what other structures could explain the same data. If an alternative fits equally well, further experiments or derivatives are needed. Unexplained peaks may be impurities or artefacts, but they must be explained, not ignored.

This order works because each stage uses the confident results of the previous one. HSQC first prevents mistaking a proton for another with a similar shift; COSY before HMBC avoids over-interpreting ambiguous long-range peaks.

Step-by-step reasoning

1. Formula and unsaturation from mass spectrometry. 2. HSQC: pair each proton with its carbon; find quaternary carbons. 3. COSY/TOCSY: assemble spin-system fragments. 4. HMBC: join fragments through protonless atoms. 5. NOESY/ROESY and J values: relative configuration. 6. Verify every correlation and consider alternatives.

Visual explanation

Picture a jigsaw. HSQC hands you the pieces labelled with both a proton and a carbon number. COSY clicks neighbouring pieces into short strips. HMBC shows which strips meet at blank pieces with no protons. NOESY finally tells you which way up the finished picture sits.

Real-world analogy

Assigning a molecule resembles a detective using several independent witnesses. Each witness reliably reports one kind of fact. A conclusion is trusted only when every witness's statement fits it, and a good detective asks whether another suspect would fit equally well.

Real-world example

When a pharmaceutical company finds an unknown impurity in a drug batch, analysts isolate it and apply this exact sequence of experiments. Regulators expect the impurity's structure to be supported by a table of 2D correlations, not just a matching mass.

Why?

Why is HMBC analysed after COSY rather than first? HMBC peaks are ambiguous about bond count and can include four-bond peaks. Having reliable fragments first narrows the possible interpretations of each long-range peak.

Common misconception

"If most correlations fit, the structure is right." A single unexplained HMBC or NOE peak can signal an incorrect structure. Published natural-product structures have been revised because inconvenient correlations were overlooked.

Worked example

Question: C₆H₁₂O₂ (one degree of unsaturation). ¹³C: 177, 60, 34, 19 (2C), 14 ppm. HSQC: 4.12/60 (CH₂), 2.52/34 (CH), 1.17/19 (CH₃, 6H), 1.26/14 (CH₃). COSY: 4.12↔1.26 and 2.52↔1.17. HMBC: 4.12→177; 1.17→177, 34. Assign the structure.

Reasoning: The 177 ppm carbon has no HSQC peak: an ester C=O. Fragment A is OCH₂CH₃ (60 and 14 ppm). Fragment B is (CH₃)₂CH, a doublet 6H methyl pair on a CH. HMBC links OCH₂ to C=O across oxygen (three bonds) and the isopropyl methyls to C=O (three bonds).

Answer: Ethyl 2-methylpropanoate, (CH₃)₂CHC(=O)OCH₂CH₃.

Quick check

1. Which experiment reveals quaternary carbons most directly, and how are they then placed in the structure? Answer: Comparing ¹³C with HSQC reveals them (no HSQC peak); HMBC correlations from nearby protons place them.

Exam focus

Present a logical order of experiments and justify it. For data problems, tabulate shifts and correlations, build fragments explicitly, and show which HMBC peak links which fragment. Always verify the final structure against all data.

Advanced insight

Computer-assisted structure elucidation (CASE) systems treat each correlation as a constraint and enumerate all structures consistent with them, often revealing alternatives a chemist missed. Combining NMR with calculated ¹³C shifts by density functional theory, and statistical comparison such as DP4 probability, gives quantitative confidence when choosing between diastereomers.

Summary

A robust assignment moves from formula and 1D inventory to HSQC, COSY/TOCSY, HMBC and finally NOESY/ROESY. Each stage uses secure results from the last. HSQC attaches protons to carbons, COSY builds fragments, HMBC joins them across protonless atoms and NOESY sets relative configuration. Verification against every observation, and a search for alternatives, completes the process.

Practice questions

1. Why is the degree of unsaturation calculated before looking at 2D spectra? Answer: It sets how many rings and π bonds the structure must contain, constraining which fragment combinations are possible. 2. A proton at 5.1 ppm shows no HSQC peak. What might it be? Answer: A proton on a heteroatom, such as an OH or NH, rather than on carbon. 3. How would you decide whether a disubstituted alkene is E or Z? Answer: Measure ³J(HH) across the double bond: about 12–18 Hz indicates E, about 6–12 Hz Z; NOESY contacts can confirm. 4. Why should an unexplained HMBC peak not simply be dismissed? Answer: It may reveal an incorrect connectivity; only after ruling out a structural cause should it be attributed to an impurity or artefact.